login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A308412 Indices of Gaussian primes on a square spiral. 1
3, 5, 7, 9, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 52, 54, 60, 62, 68, 70, 76, 78, 82, 84, 88, 90, 92, 94, 98, 100, 102, 104, 108, 110, 112, 114, 118, 120, 122, 126, 128, 132, 134, 138, 140, 144, 146, 150, 152, 156, 158 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

These are the numbers k > 0 such that A174344(k) + i*A274923(k) is a Gaussian prime (where i denotes the imaginary unit).

For symmetry reasons, we obtain the same sequence when considering a clockwise or a counterclockwise square spiral, or when initially moving towards any unit direction.

All terms except the first four are even.

LINKS

Table of n, a(n) for n=1..61.

Rémy Sigrist, PARI program for A308412

Eric Weisstein's World of Mathematics, Gaussian Prime

EXAMPLE

The first terms displayed on the center of a counterclockwise square spiral are:

  y\x|    -5   -4   -3   -2   -1    0   +1   +2   +3   +4   +5

  ---+--------------------------------------------------------

   +5|     *--100----*---98----*----*----*---94----*---92----*

     |     |                                                 |

   +4|   102    *----*----*---62----*---60----*----*----*   90

     |     |    |                                       |    |

   +3|     *    *    *---36----*---34----*---32----*    *    *

     |     |    |    |                             |    |    |

   +2|   104    *   38    *---16----*---14----*   30    *   88

     |     |    |    |    |                   |    |    |    |

   +1|     *   68    *   18    5----*----3   12    *   54    *

     |     |    |    |    |    |         |    |    |    |    |

    0|     *    *   40    *    *    *----*    *   28    *    *

     |     |    |    |    |    |              |    |    |    |

   -1|     *   70    *   20    7----*----9---10    *   52    *

     |     |    |    |    |                        |    |    |

   -2|   108    *   42    *---22----*---24----*---26    *   84

     |     |    |    |                                  |    |

   -3|     *    *    *---44----*---46----*---48----*----*    *

     |     |    |                                            |

    4|   110    *----*----*---76----*---78----*----*----*---82

     |     |

    5|     *--112----*--114----*----*----*--118----*--120----*

PROG

(PARI) See Links section.

CROSSREFS

Cf. A174344, A274923.

Sequence in context: A214315 A249098 A287774 * A327254 A054684 A294601

Adjacent sequences:  A308409 A308410 A308411 * A308413 A308414 A308415

KEYWORD

nonn

AUTHOR

Rémy Sigrist, Jun 01 2019

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 22 01:46 EDT 2020. Contains 337948 sequences. (Running on oeis4.)